Depending on the applications, one can also couple ROMs with additional parameterization schemes or surrogate models for some of the unresolved scales in order to recover more dynamical features of the original system, especially when the ROMs are constructed for under-resolved dynamical regimes.
For instance, in the context of data assimilation, when observations are only available for the (large-scale) low-frequency modes, one can design computationally efficient strategies within the conditional Gaussian framework [1]}, [2]}, [3]} to approximate the dynamics of the high-frequency (unresolved) modes with quantified uncertainties by a suitable dynamical model for the unresolved modes.
